Question

simplify the expression \\(\frac{-3h^3}{(3h^{-5})^2}\\)

Explanation:

Step1: Simplify the denominator

First, we simplify the denominator \((3h^{-5})^{2}\) using the power of a product rule \((ab)^n = a^n b^n\) and the power of a power rule \((a^m)^n = a^{mn}\). So, \((3h^{-5})^{2}=3^{2}\times(h^{-5})^{2}=9h^{-10}\).

Step2: Rewrite the expression

Now our expression becomes \(\frac{-3h^{3}}{9h^{-10}}\). We can simplify the coefficients and use the quotient rule for exponents \(\frac{a^m}{a^n}=a^{m - n}\). First, simplify the coefficients: \(\frac{-3}{9}=-\frac{1}{3}\). Then, for the variables, we have \(h^{3-(-10)} = h^{13}\).

Step3: Combine the results

Combining the coefficient and the variable part, we get \(-\frac{1}{3}h^{13}\).

Answer:

\(-\frac{1}{3}h^{13}\)